Nuclei moving through magnetized materials at high velocities are subject to very intense transient magnetic fields, resulting from the ion-solid interaction in the polarized material. The transient field has been used for g-factor measurements of short-lived nuclear states for more than a decade. Still the origin of the field is not fully explained. The present paper presents a detailed discussion of the inherent assumptions of a model based on polarized bound electrons (PBE). The contact fields from unpaired s electrons are calculated for all ions, and a number of possible polarization mechanisms are discussed in detail. Extensive studies of K-shell populations of light ions, from 0 through S, penetrating ferromagnetic solids are summarized, referring to a separate paper for details. Based on these known K-shell populations the PBE model, including a contribution from scattered polarized electrons, is compared with all available data for ions of C through S in magetized iron, cobalt, nickel, and gadolinium. The quantative agreement with the data is found to be very good if all ionic electrons are assumed to be polarized to a degree of 0.14 and 0.20 in iron and gadolinium, respectively. Furthermore, simple estimates based on the PBE model are found to reproduce the gross features of the transient field for heavier ions in iron as well as gadolinium. The processes responsible for the polarization of the deeply bound electrons are, however, still not understood in detail.